Subwavelength resonances of encapsulated bubbles

Habib Ammari, Brian Fitzpatrick, Erik Orvehed Hiltunen, Hyundae Lee, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The aim of this paper is to derive an original formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance can be efficiently computed using the multipole method. The approach involves the use of a pole-pencil decomposition of the leading order term in the asymptotic expansion of some integral operator in terms of the thickness of the coating, followed by the application of the generalized argument principle to find the characteristic value. This approach is quite general and can be applied to other subwavelength resonators such as coated plasmonic nanoparticles.

Original languageEnglish
Pages (from-to)4719-4744
Number of pages26
JournalJournal of Differential Equations
Issue number8
Publication statusPublished - 2019 Oct 5
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.


  • Bubble
  • Encapsulated bubble
  • Subwavelength resonance
  • Thin coating

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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